Question

linda thinks of a two digit number. the sum of the digits is 8. if she reverses the digits, the new number is 26 greater than her original number.

Answer 1

Let
x = the 10s digit
y = the units
N1----------> original number
N2----------> new number
N2=N1+36--------- >N2-N1=36
y+x=8------------- > equation (I)
then
10x + y = N1
10y+x=N2

(10y+x)-(10x+y)=36- -----> 9y-9x=36------- > y-x=4----------- > equation (II)

resolving (I) and (II)
 y+x=8
 y- x=4
-----------------
2y+0x=12--------------- >y=6
then
x=8-y=8-6=2----------> x=2

N1=26 and N2=62

the two digit number is 26